One specific Simultaneous ORTH for a design problem?

[dakinc]

Dear Ngene team and users,
I have a question about generating orthogonal designs in Ngene. I want to compare the performance of the Simultaneous Orthogonal Designs and Sequential Orthogonal Designs for a design problem 2^6 / 16 choice sets / 2 alternatives. Ngene can generate many different Sequential Orthogonal designs, however it always gives one specific Simultaneous Orthogonal design. With SAS macro %mktex, many different Simultaneous Orthogonal designs can be generated. Why does Ngene give only one specific Simultaneous Orthogonal design?
I hope my question is clear and makes sense.
Thanks in advance,
Deniz

[johnr]

Hi Deniz

It will depend on how you specify your syntax, as to what output the program generates. For example

Design
;alts = alt1, alt2
;rows = 12
;orth = sim
;model:
U(alt1) = b1 + b2 * A[0,1] + b3 * B[0,1] /
U(alt2) = b2 * A + b4 * C[2,4,6,8] $

Does not specify any efficiency measure to optimise on, so it will simply give you the first orthogonal design it can find.

Design
;alts = alt1, alt2
;rows = 12
;eff=(mnl,d)
;orth = sim
;model:
U(alt1) = b1 + b2 * A[0,1] + b3 * B[0,1] /
U(alt2) = b2 * A + b4 * C[2,4,6,8] $

Specifies an efficiency measure (d-error), but no priors (so they are set to zero). It will attempt to find the most efficient orthogonal design possible, however it is probable that given the zero priors, the logit probabilities become constants = 1/J and the model approximates a linear model, all orthogonal designs are equally optimal. In this case, again, the program will not be able to locate a better orthogonal design than the first reported.

In the following, non-zero priors are specified as well as an efficiency measure, and the design will likely be able to locate a more efficient orthogonal design. In this case, the program will report each new improved (in terms of efficiency) orthogonal design.

Design
;alts = alt1, alt2
;rows = 12
;eff=(mnl,d)
;orth = sim
;model:
U(alt1) = b1[0.6] + b2[-0.2] * A[0,1] + b3[-0.4] * B[0,1] /
U(alt2) = b2 * A + b4[-0.1] * C[2,4,6,8] $

So to specifically answer your question, there are likely to be multiple orthogonal designs possible, however which design the program reports/locates, will depend on the priors and efficiency measure you specify.

John